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They are not. Exponents, powers and indices are terms used for the same thing.
This exact question is on a puzzle worksheet over rational exponents used by teachers. The answer to the puzzle is Nicole Oresme.
The rule is that you multiply the exponents. So if I have 2 squared and I want to raise it to the third power, you multiply the 2x3=6. When you multiply powers you add the exponents. When you raise exponents to a power you multiply. This works for rational exponents which can be used to represent roots as well.
you do not do anything when you add numbers with exponents. you just figure out the answer. it is only if you multiply numbers with exponents, where you add the exponents..
Fractional exponents follow the same rules as integral exponents. Integral exponents are numbers raised to an integer power.